The present invention relates to a resonator and a filter using the same. More specifically, the invention relates to a technology for implementing an electro-mechanical filter circuit having high performance by using mechanical resonance, in an electrical circuit which is integrated in the high density.
A mechanical resonator according to the related art will be described with reference to FIG. 15. FIG. 15 is a diagram illustrating a simplified structure of a mechanical vibration filter (see Non-Patent Document 1) using flexible vibration.
The mechanical vibration filter according to the related art is obtained by forming a pattern on a silicon substrate by means of a thin film forming process. The mechanical vibration filter includes an input line 104, an output line 105, both-end supported beams 101 and 102 which are disposed with a gap of 1 micron or less with respect to the respective lines 104 and 105, and a coupling beam 103 which couples the two both-end supported beams 101 and 102. In addition, an input signal is input to the input line 104. The signal which is input to the input line 104 is capacitively coupled with the both-end supported beam 101 and generates an electrostatic force in the both-end supported beam 101. In only a case when a frequency of the input signal is approximately equal to a resonance frequency of an elastic structure including the both-ended supported beams 101 and 102 and the coupling beam 103, mechanical vibration is excited. Further, the mechanical vibration is detected as a variation in capacitance between the output line 105 and the both-end supported beam 102, which extracts an output signal obtained by filtering the input signal.
In the case of a both-end supported beam having a rectangular section, if the elastic modulus is set to E, the density is set to ρ, the thickness is set to h, and the length is set to L, a resonance frequency f of flexible vibration is represented as the following Equation.
                    f        =                  1.03          ⁢                                          ⁢                      h                          L              2                                ⁢                                    E              ρ                                                          [                  Equation          ⁢                                          ⁢          1                ]            
In the case where a polysilicon material is used, if the conditions E=160 GPa, ρ=2.2×103 kg/m3, L=40 μm, and h=1.5 μm are set, f becomes 8.2 MHz, and thus a filter of a band of about 8 MHz can be formed. As compared with a filter that is composed of a passive circuit, such as a capacitor or a coil, since the mechanical resonance filter uses mechanical resonance, it is possible to obtain steep frequency selection characteristics with a high Q value.
However, in the above-described structure, in forming a filter of a high frequency band, the following restriction exists. That is, as apparent from Equation 1, it is preferable that a material capable of increasing E/ρ is first used. However, if E is increased, even though a force bending the beam is the same, the displacement of the beam may be smaller. As a result, it becomes difficult to detect the displacement of the beam. Further, if the index indicating the flexibility of the beam is set to a ratio d/L between the bent amount d of the central portion of the beam and the length L of the beam when a static load is applied to the surface of the both-ended beam, d/L can be represented by a proportional relationship of the following Equation.
                              d          L                ∝                                            L              3                                      h              3                                ·                      1            E                                              [                  Equation          ⁢                                          ⁢          2                ]            
From this point, in order to raise the resonance frequency while the d/L value is maintained, a material having small density ρ needs to be selected without changing at least E. As a material that has small density in the same Young's modulus as the polysilicon, it is necessary to use a composite material, such as CFRP (Carbon Fiber Reinforced Plastics). In this case, it becomes difficult to form a minute mechanical vibration filter with a semiconductor process.
Accordingly, as a second method in which the above-described composite material is not used, there is a method in which the dimension of the beam is changed to increase h·L−2 in Equation 1. However, the increase of the thickness h of the beam and the decrease of the length L of the beam may decrease d/L in Equation 2, which is the index of the flexibility. As a result, it becomes difficult for the flexibility of the beam to be detected.
If the relationship between log (L) and log (h) is shown in FIG. 16 in regards to Equations 1 and 2, a straight line 191 indicates a relationship that is calculated from Equation 1 and a straight line 192 indicates a relationship that is calculated from Equation 2. In FIG. 16, if setting L and h in a range (region A) on the straight line of the inclination ‘2’ on the basis of the current dimension A, f is increased, and if setting L and h in a range (region B) below the straight line of the inclination ‘1’ on the basis of the current dimension A, d/L is increased. Accordingly, in FIG. 16, the hatched portion (region C) indicates a range of L and h where the resonance frequency can be raised while the bent amount of the beam is ensured.
It can be apparent from FIG. 16 that, when the frequency of the mechanical vibration filter increases, the decrease in the length L of the beam and the thickness h of the beam becomes necessary conditions, and the decrease of L and h by the same scale ratio, that is, the decrease of L and h while L and h cross the straight line of the inclination ‘1’ becomes a sufficient condition of the hatched portion of FIG. 16. As such, in the mechanical resonator according to the related art, the dimension of the mechanical vibrator is reduced and thus resonance frequency is increased.
[Non-Patent Document 1] Frank D. Bannon III, John R. Clark, and Clark T.-C. Nguyen, “High-Q HF Microelectromechanical Filters”, IEEE Journal of Solid-State Circuits, Vol. 35, No. 4, pp. 512-526, April 2000.
However, if the size of the mechanical vibrator is reduced, even though the relative ratio of d and L can be ensured, the absolute amount of d is extremely reduced. It means that at the same time as the capacitance between the electrode and the vibrator being extremely reduced, the variation in the capacitance due to the vibration becomes extremely reduced. A parasitic capacitance that is parasitic in parallel to the capacitance between the electrode and the vibrator is almost constant without depending on the size of the mechanical vibrator. If the parasitic capacitance becomes larger than the capacitance between the electrode and the vibrator, when the mechanical vibrator becomes smaller, the variation in electrical impedance of the vibrator at the resonance point may be smaller. As a result, the sensitivity is lowered, and a filter operation becomes insufficient.
Accordingly, as disclosed in Non-Patent Document 2 or 3, a method has been investigated in which amplitude of a vibrator is increased by using parametric resonance. That is, in addition to an exciting force applied to the vibrator from the outside, modulation is performed on a spring property of the vibrator or mass, which allows an effect of amplifying amplitude near a resonance point. The description is made using the related art shown in FIG. 15. If the vibration of the both-ended beams 101 and 102 of the resonator is amplified, since a current proportional to the vibration velocity flows through the output line 105, it is possible to obtain an output signal having a superior S/N ratio. When the vibrator is very tiny, that is, when a frequency at the vibrator is increased, it contributes to attain the effect.
Accordingly, as disclosed in Non-Patent Document 2 or 3, analysis of occurrence conditions of the uncontrollable oscillation state or non-linear jump of the vibration spectrum has been investigated. The phenomenon, such as the uncontrollable oscillation or non-linear jump, is inappropriate when the resonator is applied to the filter. Further, the consideration is not being made in terms of whether an optimal value exists in the relationship between the modulation of the spring property and the phase of the external exciting force.